АНАЛИЗ ЭФФЕКТИВНОСТИ МЕНЕДЖМЕНТА ПОДРАЗДЕЛЕНИЙ

Èííîâàòèêà è ýêñïåðòèçà. 2015. Âûïóñê 2 (15)
АНАЛИЗ ЭФФЕКТИВНОСТИ МЕНЕДЖМЕНТА ПОДРАЗДЕЛЕНИЙ
НЕПОСРЕДСТВЕННОЙ РЕАЛИЗАЦИИ УЧЕБНОГО ПРОЦЕССА
УЧРЕЖДЕНИЙ ВЫСШЕГО ПРОФЕССИОНАЛЬНОГО ОБРАЗОВАНИЯ
С ПОМОЩЬЮ ЭТАЛОНОВ
Â.Î. Ãðîïïåí, çàâ. êàô. Ñåâåðî-Êàâêàçñêîãî ãîðíî-ìåòàëëóðãè÷åñêîãî èíñòèòóòà
(ÃÒÓ), äèðåêòîð ÍÈÈ Òåîðåòè÷åñêîé è Ïðèêëàäíîé Èíôîðìàòèêè (ÍÈÈÒÏÈ),
ä-ð òåõí. íàóê, ïðîô., groppen@mail.ru
À.À. Áóäàåâà, äîö. êàô. Ñåâåðî-Êàâêàçñêîãî ãîðíî-ìåòàëëóðãè÷åñêîãî èíñòèòóòà
(ÃÒÓ), êàíä. òåõí. íàóê, budalina@yandex.ru
 ðàáîòå ïðåäëàãàåòñÿ èñïîëüçîâàòü ìàòåìàòè÷åñêèé àïïàðàò äëÿ îöåíêè ýôôåêòèâíîñòè ìåíåäæìåíòà ïîäðàçäåëåíèé è ó÷àñòíèêîâ íåïîñðåäñòâåííîé ðåàëèçàöèè ó÷åáíîãî
ïðîöåññà, îñíîâó êîòîðîãî ñîñòàâëÿþò ðàíæèðîâàíèå è ïðîãíîçèðîâàíèå. Ê äîñòîèíñòâàì
ïðåäëàãàåìîãî ïîäõîäà ìîæíî îòíåñòè åãî èíâàðèàíòíîñòü îòíîñèòåëüíî èñïîëüçóåìîé
ñèñòåìû ïîêàçàòåëåé è íåçàâèñèìîñòü îò ñóáúåêòèâíîãî ìíåíèÿ ëèö, ïðèíèìàþùèõ ðåøåíèå. Ïðèâîäÿòñÿ ïðèìåðû, èëëþñòðèðóþùèå ðåàëèçàöèþ îñíîâíûõ ýòàïîâ ïðåäëàãàåìîãî
ïîäõîäà.
Êëþ÷åâûå ñëîâà: îöåíêà ýôôåêòèâíîñòè, êðèòåðèè, ðàíæèðîâàíèå, ïðîãíîçèðîâàíèå,
ýòàëîí.
THE ANALYSIS OF EFFICIENCY OF MANAGEMENT OF DIVISIONS OF
DIRECT REALIZATION OF EDUCATIONAL PROCESS OF INSTITUTIONS
OF HIGHER PROFESSIONAL EDUCATION BY MEANS OF REFERENCE
STANDARDS
V.Î. Groppen, Head of the Chair, North Caucasian Mining and Metallurgical Institute
(NCMMI), Director of Scientific Research Institute of Theoretical and Applied Informatics
(NIITPI), Ph.D. of Engineering, Professor, groppen@mail.ru
À.À. Budayeva, Assistant Professor of Chair, North Caucasian Mining and Metallurgical
Institute (NCMMI), Doctor of Engineering, budalina@yandex.ru
We propose to use a mathematical tool for evaluating the effectiveness of management units and
members of the immediate implementation of the training, which is based on ranking and forecasting.
The advantages of the proposed approach can be attributed to the invariance under the system’s
indicators and independence from the subjective opinion of decision-makers. The examples illustrate
the main stages of implementation of the proposed approach.
Keywords: performance evaluation, criteria, ranking, forecasting model.
Ââåäåíèå
Öåëÿìè îöåíêè ýôôåêòèâíîñòè ìåíåäæìåíòà ïîäðàçäåëåíèé è ó÷àñòíèêîâ íåïîñðåäñòâåííîé ðåàëèçàöèè ó÷åáíîãî ïðîöåññà ÿâëÿþòñÿ îïðåäåëåíèå ðåéòèíãà ïðåïîäàâàòåëåé, êàôåäð, äåêàíàòîâ, ôèëèàëîâ è ò. ï. êàê íà îñíîâàíèè êàæäîãî èñïîëüçóåìîãî êðèòåðèÿ, òàê è
èíòåãðàëüíî, ñ îäíîâðåìåííûì ó÷åòîì âñåõ êðèòåðèåâ. Òàêîé ïîäõîä ïîçâîëÿåò íå òîëüêî
îïðåäåëèòü ìåñòî â èíòåãðàëüíîì ðåéòèíãå êàæäîãî îáúåêòà, íî è âûñâåòèòü ïðè÷èíû, ïðèâåäøèå ê òàêîìó ðåçóëüòàòó.  ñëó÷àå ðàíæèðîâàíèÿ îäíîâðåìåííî ïî ðÿäó ïîêàçàòåëåé
çàäà÷à ÿâëÿåòñÿ ìíîãîêðèòåðèàëüíîé, îäíàêî íåïîñðåäñòâåííîå èñïîëüçîâàíèå ïðèíöèïà
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Ïàðåòî ïðè ðåøåíèè ïðèêëàäíûõ çàäà÷ ÷àñòî îñëîæíÿåòñÿ ìíîæåñòâåííîñòüþ ñî÷åòàíèé
çíà÷åíèé êðèòåðèåâ, ÿâëÿþùèõñÿ îïòèìàëüíûìè [1, 2]. Ïîñëåäíåå ïðèâîäèò ê åñòåñòâåííîìó ñòðåìëåíèþ ê ïåðåõîäó ê îäíîêðèòåðèàëüíîé çàäà÷å ðàíæèðîâàíèÿ, ÷òî ñâÿçàíî ñ âûáîðîì òåõíîëîãèè ñâåðòêè. Ïîñêîëüêó íàèáîëåå ÷àñòî èñïîëüçóåìûå ìåòîäû ñâåðòêè êðèòåðèåâ – èõ ëåêñèêîãðàôè÷åñêîå óïîðÿäî÷åíèå ëèáî èõ âçâåøåííàÿ ñóììà íå ñâîáîäíû îò ñóáúåêòèâíîãî ìíåíèÿ ëèö, ïðèíèìàþùèõ ðåøåíèå [3, 4], íèæå ïåðåõîä ê îäíîìó êðèòåðèþ
áàçèðóåòñÿ íà ñî÷åòàíèè ðàíæèðîâàíèÿ è ýòàëîíîâ [5–7].
¹
Íàèìåíîâàíèå
ïîêàçàòåëÿ
Êîììåíòàðèè
1
Ïîñåùàåìîñòü
Ïðîöåíò ïðîïóùåííûõ àóäèòîðíûõ ÷àñîâ, ïðèõîäÿùèõñÿ íà îäíîãî ñòóäåíòà
2
Óñïåâàåìîñòü
Ñðåäíÿÿ àðèôìåòè÷åñêàÿ îöåíêà çíàíèé â õîäå ñåññèè, ïðèõîäÿùàÿñÿ íà
îäíîãî ñòóäåíòà
3
Ïðîöåíò íèçêî
ìîòèâèðîâàííûõ
îöåíîê
Ïðîöåíò îöåíîê, ïîëó÷åííûõ â õîäå ñåññèè è ñóùåñòâåííî îòëè÷àþùèõñÿ
îò îöåíîê çíàíèé ñòóäåíòîâ, ïîëó÷åííûõ â ðàìêàõ ðóáåæíîãî êîíòðîëÿ è
èíûõ ñïîñîáîâ òåêóùåãî êîíòðîëÿ â õîäå ñåìåñòðà
4
Äèíàìèêà
òåêóùåé
óñïåâàåìîñòè
Ïðîöåíò ñëó÷àåâ, êîãäà òåêóùèé è ðóáåæíûé êîíòðîëü çíàíèé ñòóäåíòîâ â
õîäå ñåìåñòðà íå âûÿâëÿåò èõ ïîëîæèòåëüíîé äèíàìèêè, ò. å. êîãäà íèçêàÿ
óñïåâàåìîñòü â ïåðâîé ïîëîâèíå ñåìåñòðà íå ïðèâåëà ê èñïîëüçîâàíèþ
ýôôåêòèâíûõ ïîäõîäîâ, ïðèâîäÿùèõ ê ïîëîæèòåëüíîé äèíàìèêå îöåíîê
Îñîáåííîñòè ïðèìåíåíèÿ ýòàëîíîâ â ìíîãîêðèòåðèàëüíîì ðàíæèðîâàíèè
Êàê ïðàâèëî, äëÿ îöåíêè ýôôåêòèâíîñòè ìåíåäæìåíòà ïîäðàçäåëåíèé è ó÷àñòíèêîâ íåïîñðåäñòâåííîé ðåàëèçàöèè ó÷åáíîãî ïðîöåññà èñïîëüçóþòñÿ íåîäíîðîäíûå ïîêàçàòåëè, îáùåé ÷åðòîé êîòîðûõ ÿâëÿåòñÿ èõ êîëè÷åñòâåííûé õàðàêòåð. Íèæå, â òàáëèöå, ïåðå÷èñëåíû
íåêîòîðûå èç íèõ.
Äàëåå áóäåì ïîëàãàòü, ÷òî äëÿ êàæäîãî i-ãî êðèòåðèÿ Êi íå ñîñòàâëÿåò òðóäà îïðåäåëèòü
åãî âåðõíþþ Ki max è íèæíþþ Ki min ãðàíèöû. Íàïðèìåð, ïðîöåíò ïðîïóùåííûõ îäíèì
ñòóäåíòîì àóäèòîðíûõ ÷àñîâ çàêëþ÷åí â äèàïàçîíå {0 – 100}, à ñðåäíèé áàëë ñòóäåíòà îïðåäåëÿåòñÿ äèàïàçîíîì {2–5}. Ýòî ïîçâîëÿåò ïåðåéòè îò èñõîäíûõ êðèòåðèåâ ê èõ íîðìèðîâàííûì àíàëîãàì Fi, ïîëüçóÿñü óðàâíåíèåì:
∀i : Fi =
Ki − Ki min
.
Ki max − Ki min
(1)
Ñïðàâåäëèâà ñëåäóþùàÿ òåîðåìà:
Òåîðåìà 1. Îïòèìàëüíîå ðàíæèðîâàíèå îáúåêòîâ íà îñíîâàíèè ìíîæåñòâà êðèòåðèåâ {Fi}
ñîâïàäàåò ñ îäíèì èç îïòèìàëüíûõ ïî Ïàðåòî ðàíæèðîâàíèé òåõ æå îáúåêòîâ íà îñíîâàíèè
ìíîæåñòâà êðèòåðèåâ {Ki}.
Äîêàçàòåëüñòâî òåîðåìû ïðèâîäèòñÿ â [5].
Äëÿ òîãî, ÷òîáû âîñïîëüçîâàòüñÿ òåîðåìîé 1, îáîçíà÷èì ñèìâîëîì Fi opt îïòèìàëüíûå
çíà÷åíèÿ êðèòåðèåâ Fi, i = 1,2,...n, è îïðåäåëèì «èäåàëüíûé» îáúåêò, ýòàëîí, äëÿ êîòîðîãî
ñïðàâåäëèâî: Fi = Fi opt, i = 1,2,...n. Ðåàëüíî òàêîãî îáúåêòà ìîæåò íå ñóùåñòâîâàòü, îäíàêî
ýòî ïîçâîëÿåò ðàíæèðîâàòü îñòàëüíûå îáúåêòû ïî âîçðàñòàíèþ «ðàññòîÿíèÿ» òî÷åê, îòâå÷àþùèõ ðàíæèðóåìûì îáúåêòàì â ïðîñòðàíñòâå êðèòåðèåâ, îò ýòàëîíà (ðèñ. 1).
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ɉɪɨɰɟɧɬ ɧɢɡɤɨɦɨɬɢɜɢɪɨɜɚɧɧɵɯ ɨɰɟɧɨɤ
Ɏ1
1
Ɏ2
ɗɬɚɥɨɧ
0
Ɏ2
Ɏ1
1
2
n
1
ɍɫɩɟɜɚɟɦɨɫɬɶ
1
ɉɨɫɟɳɚɟɦɨɫɬɶ
Ðèñ. 1. Ðàíæèðîâàíèå äâóõ ôàêóëüòåòîâ Ô1 è Ô2
ïî òðåì íîðìèðîâàííûì êðèòåðèÿì îòíîñèòåëüíî ýòàëîíà
Ïðîãíîç òåíäåíöèé
Ïðè ïåðåâûáîðàõ ïðåïîäàâàòåëåé âóçîâ, çàâ. êàôåäðàìè, äåêàíîâ è ò. ï., îñîáîå çíà÷åíèå
ïðèîáðåòàåò ïðîãíîç ýôôåêòèâíîñòè èñïîëüçóåìûõ èìè â ïðîôåññèîíàëüíîé äåÿòåëüíîñòè
òåõíîëîãèé [8]. Â ðàìêàõ ïðåäëàãàåìîãî ïîäõîäà ïîâòîðåíèå ïðîöåäóðû ðàíæèðîâàíèÿ íà
ïðîòÿæåíèè ðÿäà ëåò ïîçâîëÿåò îïðåäåëèòü ãðàôè÷åñêè äèíàìèêó ìåñòà â ðåéòèíãå ïî âûáðàííîìó êðèòåðèþ (ðèñ. 2), à ïî íåé, àïïðîêñèìèðóÿ ïîëó÷åííóþ çàâèñèìîñòü àíàëèòè÷åñêè, îïðåäåëèòü ïðîãíîç íà ïëàíèðóåìûé ïåðèîä. Òàê, ïðèìåíèòåëüíî ê ôàêóëüòåòó Ô9
(ðèñ. 2), àïïðîêñèìàöèÿ ñ ïîìîùüþ ìåòîäà íàèìåíüøèõ êâàäðàòîâ çàâèñèìîñòè «èíòåãðàëüíûé êðèòåðèé/ãîä» ïîëèíîìîì âòîðîãî ïîðÿäêà:
Ì = – 9.940358∙10
–5
– 0.3458189∙Ò + 1.737061∙10–4∙Ò2 ,
(2)
ãäå Ì – ìåñòî ôàêóëüòåòà Ô9 ïî èíòåãðàëüíîìó êðèòåðèþ, Ò – ãîäû (îò 2010 äî 2014), ïîçâîëÿåò
ïðîãíîçèðîâàòü «ôèêñàöèþ» ýòîãî ôàêóëüòåòà â ðåéòèíãå ôàêóëüòåòîâ âóçà ïî âûøåíàçâàííîìó
êðèòåðèþ íà îäíîì èç ïîñëåäíèõ ìåñò â 2015 ã.
ˇ1
ˇ2
ˇ3
ˇ4
ˇ5
ˇ6
ˇ7
ˇ8
ˇ9
0
1
2
3
4
5
6
7
8
9
10
2009
2010
2011
2012
2013
2014
2015
Ðèñ. 2. Ïðèìåð ðàíæèðîâàíèÿ äåâÿòè ôàêóëüòåòîâ âóçà íà ïðîòÿæåíèè
ïîñëåäíèõ ïÿòè ëåò ïî èíòåãðàëüíîìó ïîêàçàòåëþ
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Çàêëþ÷åíèå
Îïèñàííûé âûøå ïîäõîä ê àíàëèçó ýôôåêòèâíîñòè ôóíêöèîíèðîâàíèÿ ïîäðàçäåëåíèé è
ó÷àñòíèêîâ íåïîñðåäñòâåííîé ðåàëèçàöèè ó÷åáíîãî ïðîöåññà ïîíèæàåò ñóáúåêòèâèçì â
îöåíêàõ òàêîãî ðîäà. Ê åãî äîñòîèíñòâàì òàêæå ñëåäóåò îòíåñòè íåçàâèñèìîñòü îò ÷èñëà è
ñïåöèôèêè èñïîëüçóåìûõ ïîêàçàòåëåé, à òàêæå îò ïðèìåíÿåìûõ ñïîñîáîâ àïïðîêñèìàöèè
ïîëó÷åííûõ çàâèñèìîñòåé [9]. Áîëüøîé îáúåì îáðàáàòûâàåìîé èíôîðìàöèè è âû÷èñëåíèé,
ñâÿçàííûå ñ åãî ïðèìåíåíèåì, ìîãóò îáåñïå÷èâàòüñÿ ïîäñèñòåìàìè ÀÑÓ âóç, ÷òî îáëåã÷àåò
åãî ðåàëèçàöèþ è âíåäðåíèå. Ìîæíî òàêæå îòìåòèòü ýôôåêòèâíîñòü àíàëîãè÷íîãî ïðèìåíåíèÿ îïèñàííîãî âûøå ïîäõîäà â äðóãèõ ïðåäìåòíûõ îáëàñòÿõ [7, 10, 11].
Ñïèñîê ëèòåðàòóðû
1. Ãðîïïåí Â.Î. Ïðèíöèïû îöåíêè êà÷åñòâà ðåøåíèÿ ìíîãîêðèòåðèàëüíûõ îïòèìèçàöèîííûõ çàäà÷ ñ ïîìîùüþ ýòàëîíîâ. Ìàòåðèàëû V Ìåæäóíàðîäíîé êîíôåðåíöèè «Óñòîé÷èâîå ðàçâèòèå ãîðíûõ
òåððèòîðèé: ïðîáëåìû è ïåðñïåêòèâû èíòåãðàöèè íàóêè è îáðàçîâàíèÿ», 21–23.09.2004 ã., ñòð. 572–580.
2. Ãðîïïåí Â.Î. Ðåøåíèå çàäà÷ ìíîãîêðèòåðèàëüíîé îïòèìèçàöèè è ðàíæèðîâàíèÿ îáúåêòîâ
ìåòîäîì ýòàëîíîâ. Òåëåêîìì. èíô. îáðàç. M., ¹ 2 (33), ìàðò–àïðåëü, 2006, ñòð. 14–31.
3. Ëàðè÷åâ Î.È. Òåîðèÿ è ìåòîäû ïðèíÿòèÿ ðåøåíèé. Ì. Ëîãîñ, 2000.
4. Ïîäèíîâñêèé Â.Â. Ââåäåíèå â òåîðèþ âàæíîñòè êðèòåðèåâ â ìíîãîêðèòåðèàëüíûõ çàäà÷àõ ïðèíÿòèÿ ðåøåíèé. ÔÈÇÌÀÒËÈÒ, 2007.
5. Groppen V.O. (2004) New Solution Principles of Multi-Criteria Problems Based on Comparison
Standards. Available at: http//:www.arxiv.org/ftp/math/papers/0501/0501357.pdf.
6. Ãðîïïåí Â.Î. Ïðèíöèïû ïðèíÿòèÿ ðåøåíèé ñ ïîìîùüþ ýòàëîíîâ. Èçä. ÐÀÍ, Àâòîìàòèêà è
òåëåìåõàíèêà, ¹ 4, 2006, ñòð. 167–184.
7. Groppen V.O. New Solution Principle for Multi-criteria Problems Based on Comparison Standards: Models, Algorithms, Applications. Programme and Abstracts Eurogen 2007. Evolutionary and Deterministic Methods
for Design, Optimization and Control with Applications to Industrial and Societal Problems. 11–13 June 2007
Jyvaskyla, Finland, pp. 100–101.
8. Îðëîâ À.È. Òåîðèÿ ïðèíÿòèÿ ðåøåíèé. Ì.: Èçäàòåëüñòâî «Ìàðò», 2004.
9. Ãîëóáèíñêèé À.Í. Ìåòîäû àïïðîêñèìàöèè ýêñïåðèìåíòàëüíûõ äàííûõ è ïîñòðîåíèÿ ìîäåëåé.
Âåñòíèê Âîðîíåæñêîãî óíèâåðñèòåòà ÌÂÄ Ðîññèè, ¹ 2, 2007.
10. Âàãèí Â.Ñ., Ãðîïïåí Â.Î., Ïîçäíÿêîâà Ò.À., Áóäàåâà À.À. Ìíîãîêðèòåðèàëüíîå ðàíæèðîâàíèå
îáúåêòîâ ìåòîäîì ýòàëîíîâ êàê èíñòðóìåíò îïòèìàëüíîãî óïðàâëåíèÿ. Óñòîé÷èâîå ðàçâèòèå ãîðíûõ
òåððèòîðèé, ¹ 1, 2010, ñ. 47–56.
11. Ãðîïïåí Â.Î., Áóäàåâà À.À. Ðàííåå ïðîãíîçèðîâàíèå ðàçâèòèÿ «öâåòíûõ ðåâîëþöèé» ñèñòåìîé
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